Prayers for vengeance
Prayers for vengeance (also Psalm 109) — the honest voice of the wronged, an ethical difficulty, and a question of Christian use; traditions differ on praying them.
Psalm 137:7-9
7Remember, Yahweh, against the children of Edom in the day of Jerusalem, who said, “Raze it! Raze it even to its foundation!”
8Daughter of Babylon, doomed to destruction, he will be happy who repays you, as you have done to us.
9Happy shall he be, who takes and dashes your little ones against the rock.
What each tradition says
Rabbinic / Midrashic
Ginzberg and Levias explain that cursing rests on a belief that spoken words can bring calamity, regardless of moral justification. They find traces of this heathen idea of a curse’s objective, mystic power in Psalm 109 and the Talmud. In general, however, the Bible sees a curse as a wish that God fulfills when it is just and deserved.
Louis Ginzberg and Caspar Levias (The Jewish Encyclopedia), The Jewish Encyclopedia, vol. 4, s.v. 'Cursing' (New York: Funk & Wagnalls, 1901-1906) — section 'Biblical Conception'
Patristic
Augustine identifies Babylon’s “little ones” as evil desires at their birth. While a lust is still small, before habit strengthens it, it should be dashed—not feared that it will not die. He says, “Dash it against the Rock; and that Rock is Christ.”
Augustine of Hippo (354-430), Expositions on the Book of Psalms (Oxford 'Library of the Fathers' translation, condensed by A. Cleveland Coxe), in Nicene and Post-Nicene Fathers, ser. 1, vol. 8 (New York: Christian Literature Publishing Co., 1888) — Exposition of Psalm 137, §12 (on verse 9)
Catholic
Walter Drum, S.J., says the imprecatory psalms are national anthems expressing a nation's wrath, not an individual's. He argues humility, meekness, and forgiveness are individual virtues, not necessarily a nation's, and by no means those of Jahweh's Chosen Nation, which knew by revelation Jahweh willed it to be great and put out its enemies from the land he gave them.
Walter Drum, S.J. (The Catholic Encyclopedia, 1911), The Catholic Encyclopedia, vol. 12, s.v. 'Psalms' (New York: Robert Appleton Company, 1911) — section on the objections to the imprecatory psalms
Orthodox
No sourced position found. Checked: John of Damascus, An Exact Exposition of the Orthodox Faith (NPNF ser. 2, vol. 9) — 'psalm' occurs only in the canonical lists and scriptural references, nothing on imprecations; the Synod of Jerusalem (1672, Confession of Dositheus, trans. Robertson, 1899) — the word 'psalm' occurs not at all in the full text; the public-domain English Chrysostom corpus (NPNF ser. 1) holds the New Testament homilies only, and the Eastern Psalm commentaries (Basil's Homilies on the Psalms, Athanasius's Letter to Marcellinus, Theodoret on the Psalms) exist in English only in modern translations under copyright; CCEL, archive.org and web searches for a public-domain English Orthodox treatment of the imprecatory psalms found none.
Reformed / Protestant
Calvin acknowledges that wishing tender and innocent infants dashed and mangled on stones may seem cruel. But he says the psalmist does not speak from personal feeling; he only uses words God authorized, declaring a just judgment, as our Lord says, "With what measure ye mete, it shall be measured to you again."
John Calvin (1509-1564), Commentary on the Book of Psalms, vol. 5 (trans. James Anderson, Calvin Translation Society, 1849) — Commentary on Psalm 137:8-9
Evangelical
John Wesley identifies the one called happy as God’s instrument. That instrument vindicates God’s honor and executes his just judgments.
John Wesley (1703-1791), Explanatory Notes upon the Old Testament (Bristol: William Pine, 1765; CCEL edition) — Note on Psalm 137:8